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Maths : Tips
Some Critical Tips : # If certain conditions are given , look for the options that satisfy the condition . # If an equation is asked then substitute the values in the option in the equation . # Use Trial and Error Method / Elimination method . # For co-ordinate geometry , draw graphs according to equations given and predict the answer . # The first step in Mathematics is mostly crucial and may require Simplification . Here are techniques of SImplifications that you should try : 1. Rationalizing 2. Plus & Minus 3. Multiplying and Dividing 4. Dividing Throughout by 5.'''Splitting the Numerator '''6. Squaring on Both Sides . Sets, Relations and Functions 1) For functions , try to plot graphs . So learn more different kinds of functions and their graphs , or else derive the graph using x-y method . 2) For Set theory draw venn diagrams for better understanding of the question . Theory of Equations # For Analyzing an equation , remember : ## If ∆ = 0 ; then there will be infinite solutions if ∆x,∆y,∆z = 0 . And there will b no solution otherwise . ## If ∆ =/= 0 ; then there will be an unique solution . ## If ∆ = 0 ; then equations will have nontrivial solution # For an equation to have no solution , the ratios of co-efficients of x , y and constant will be equal to each other . # A Monotonic Function (Increasing/Decreasing) has only one root . Complex Numbers # In order to get rid of i term , you can rationalize the question to convert i into i2 . Prefer to reach i2 . # Use Geometrical interpretation of Complex Numbers along with De Moivre's Theorem for solving geometry based questions . Sequences and Series # For Infinite Series , first find the equation of the series in general terms . Then use the Sum of /infite Series Formulae . # For AP , GP and HP ; trying out the 4 options can be helpful . Trigonometry # For General Solution , bring the equation in one of the sandard forms . This can be done by using factorization formulae (i.e. to convert from addition to multiplication) . # For Solutions of Triangle problems , the following techniques should be used : ## sin ## a2, b2,c2 ## A + B + C = 180 ## Half Angle ## Factorization formulae Co-ordinate Geometry Circle & Conics # Draw a graph with the help of given equations , to predict the answer . Limits # If the Question is of the form 0/0 , then apply L' Hospitals Rule . Differentiation and Application # For Implicit , use shortcut . # Integral Calculus and Area under Curve # For Indefinite Integration ; Differentiate the options to reach the Question . # For u.v ; use the shortcut Matrices # Do Adjoint first or transpose/square/other operation first , the answer is same . # Try to use the options for finding the answer , rather than solving the entire sum . # Use properties of determinants to simplify a given matrix . 3 Dimensional Geometry # In formulas dealing with ratios (e.g. cartesian equation of line , condition for parallel and perpendicular lines) direction ratios can be replaced with direction cosines .